What are the divisors of 5455?

1, 5, 1091, 5455

There is a total of 4 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 1638.

4 odd divisors

1, 5, 1091, 5455

How to compute the divisors of 5455?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5455 by each of the numbers from 1 to 5455 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5455 / 1 = 5455 (the remainder is 0, so 1 is a divisor of 5455)
5455 / 2 = 2727.5 (the remainder is 1, so 2 is not a divisor of 5455)
5455 / 3 = 1818.3333333333 (the remainder is 1, so 3 is not a divisor of 5455)
...
5455 / 5454 = 1.0001833516685 (the remainder is 1, so 5454 is not a divisor of 5455)
5455 / 5455 = 1 (the remainder is 0, so 5455 is a divisor of 5455)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5455 (i.e. 73.857971810767). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5455 / 1 = 5455 (the remainder is 0, so 1 and 5455 are divisors of 5455)
5455 / 2 = 2727.5 (the remainder is 1, so 2 is not a divisor of 5455)
5455 / 3 = 1818.3333333333 (the remainder is 1, so 3 is not a divisor of 5455)
...
5455 / 72 = 75.763888888889 (the remainder is 55, so 72 is not a divisor of 5455)
5455 / 73 = 74.72602739726 (the remainder is 53, so 73 is not a divisor of 5455)